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*The author of this computation has been verified*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Fri, 10 Dec 2010 12:12:44 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/10/t1291983054k6ojgs7aslvgyb5.htm/, Retrieved Fri, 10 Dec 2010 13:10:54 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/10/t1291983054k6ojgs7aslvgyb5.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

101.76 102.37 102.38 102.86 102.87 102.92 102.95 103.02 104.08 104.16 104.24 104.33 104.73 104.86 105.03 105.62 105.63 105.63 105.94 106.61 107.69 107.78 107.93 108.48 108.14 108.48 108.48 108.89 108.93 109.21 109.47 109.80 111.73 111.85 112.12 112.15 112.17 112.67 112.80 113.44 113.53 114.53 114.51 115.05 116.67 117.07 116.92 117.00 117.02 117.35 117.36 117.82 117.88 118.24 118.50 118.80 119.76 120.09

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.243728	-1.635	0.054515
2	0.138719	0.9306	0.178524
3	0.00837	0.0561	0.477735
4	0.291049	1.9524	0.028563
5	-0.103181	-0.6922	0.246197
6	-0.173061	-1.1609	0.125897
7	0.255001	1.7106	0.047021
8	-0.285695	-1.9165	0.030833
9	0.289763	1.9438	0.029095
10	-0.250304	-1.6791	0.050033
11	0.292178	1.96	0.028103
12	-0.309274	-2.0747	0.021882
13	0.146461	0.9825	0.165556
14	-0.040484	-0.2716	0.393594
15	-0.104534	-0.7012	0.243384
16	-0.055723	-0.3738	0.355153
17	-0.205059	-1.3756	0.08788
18	0.268067	1.7982	0.039424
19	-0.212837	-1.4278	0.080133
20	0.085639	0.5745	0.28425
21	-0.137971	-0.9255	0.179812
22	0.309417	2.0756	0.021836
23	-0.112567	-0.7551	0.227055
24	-0.135622	-0.9098	0.183893
25	0.048221	0.3235	0.373916
26	0.026025	0.1746	0.431095
27	-0.032728	-0.2195	0.413609
28	-0.141388	-0.9485	0.173981
29	0.163741	1.0984	0.138935
30	-0.129348	-0.8677	0.195083
31	0.031714	0.2127	0.416243
32	0.009494	0.0637	0.47475
33	-0.025533	-0.1713	0.432385
34	-0.09876	-0.6625	0.255514
35	-0.012853	-0.0862	0.465836
36	-0.000706	-0.0047	0.498122
37	-0.08916	-0.5981	0.276384
38	-0.039962	-0.2681	0.394934
39	-0.008345	-0.056	0.477801
40	0.065273	0.4379	0.331789
41	-0.048213	-0.3234	0.373936
42	0.000634	0.0043	0.498312
43	0.060518	0.406	0.343345
44	0.006749	0.0453	0.482044
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.243728	-1.635	0.054515
2	0.084325	0.5657	0.287213
3	0.064119	0.4301	0.334579
4	0.317081	2.127	0.019466
5	0.032316	0.2168	0.41468
6	-0.306899	-2.0587	0.022668
7	0.140553	0.9429	0.175395
8	-0.284631	-1.9094	0.031302
9	0.309142	2.0738	0.021926
10	-0.02482	-0.1665	0.434257
11	0.136938	0.9186	0.1816
12	-0.210219	-1.4102	0.082679
13	-0.108258	-0.7262	0.235733
14	-0.035796	-0.2401	0.405661
15	-0.037297	-0.2502	0.401787
16	-0.105714	-0.7092	0.240945
17	-0.074201	-0.4978	0.31054
18	0.059247	0.3974	0.346461
19	0.214967	1.442	0.078108
20	-0.140106	-0.9399	0.176153
21	0.056535	0.3792	0.353144
22	0.059177	0.397	0.346631
23	0.020793	0.1395	0.444846
24	-0.200883	-1.3476	0.092272
25	-0.105042	-0.7046	0.242332
26	0.102399	0.6869	0.247831
27	-0.037339	-0.2505	0.401679
28	0.099539	0.6677	0.25386
29	-0.04036	-0.2707	0.393913
30	-0.079138	-0.5309	0.299059
31	-0.090501	-0.6071	0.273418
32	-0.060934	-0.4088	0.342328
33	-0.09203	-0.6174	0.270055
34	0.069359	0.4653	0.321989
35	-0.005407	-0.0363	0.485615
36	-0.089661	-0.6015	0.275275
37	-0.007434	-0.0499	0.480225
38	0.043665	0.2929	0.385468
39	-0.046695	-0.3132	0.377774
40	0.042832	0.2873	0.38759
41	-0.145712	-0.9775	0.166781
42	0.086017	0.577	0.283402
43	0.068961	0.4626	0.322938
44	-0.088976	-0.5969	0.276793
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291983054k6ojgs7aslvgyb5/1arv81291983161.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291983054k6ojgs7aslvgyb5/1arv81291983161.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291983054k6ojgs7aslvgyb5/230db1291983161.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291983054k6ojgs7aslvgyb5/230db1291983161.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

R code (references can be found in the software module):

if (par1 == 'Default') {

par1 = 10*log10(length(x))

} else {

par1 <- as.numeric(par1)

}

par2 <- as.numeric(par2)

par3 <- as.numeric(par3)

par4 <- as.numeric(par4)

par5 <- as.numeric(par5)

if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'

par7 <- as.numeric(par7)

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

dev.off()

(myacf <- c(racf$acf))

(mypacf <- c(rpacf$acf))

lengthx <- length(x)

sqrtn <- sqrt(lengthx)

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 2:(par1+1)) {

a<-table.row.start(a)

a<-table.element(a,i-1,header=TRUE)

a<-table.element(a,round(myacf[i],6))

mytstat <- myacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:par1) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,round(mypacf[i],6))

mytstat <- mypacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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